U.S. Secretary of Antony Blinken, who is currently in Saudi Arabia, notably called for a cease-fire as "the most effective way to address the humanitarian crisis in Gaza" during a session with his counterparts of the Gulf Cooperation Council.

"The most effective way to address the humanitarian crisis in Gaza to alleviate the suffering of children, women and men and to create space for a more just and durable solution is to get a cease-fire and hostages home, but also not waiting on a cease-fire to take the necessary steps to meet the needs of civilians of Gaza," Blinken said.

"President Biden is insistent that Israel take specific concrete measurable steps to better address humanitarian suffering, civilian harm and the safety of aid workers in Gaza, including in his most recent call with Prime Minister Netanyahu," he added, referring to a Sunday call with the Israeli leader.

Blinken said the U.S. was "focused on addressing the greatest threat to regional stability and regional security -- Iran."

-ABC News' Lauren Minore

U.S. Central Command and the Royal Jordanian Air Force conducted a combined humanitarian assistance airdrop into Northern Gaza on Sunday.

The combined joint operation included Jordanian provided food and four U.S. Air Force C-130 aircraft.

The U.S. C-130's dropped over 25,000 Meals Ready to Eat (MREs), providing life-saving humanitarian assistance in Northern Gaza. Additionally, more than 13,080 meal equivalents of Jordanian food supplies were also delivered.

To date the U.S. has dropped nearly 1,110 tons of humanitarian assistance.

-ABC News’ Nate Luna

Hanna Siegel, niece of American hostage Keith Siegel, appeared on CBS' "Face the Nation" on Sunday morning and talked about the "surreal" feeling of seeing a recently released video purporting to show her uncle and talked about the possibility of a deal that would free him and other people thought to still be held by Hamas in Gaza.

"We've always believed that he was alive. We have to believe he's alive -- and his wife, my aunt, who was held for 52 days, [was] released in the deal that took place in November, she was with him," Siegel said. "When she came out, she told us he was alive, but this is the first time that we're seeing him, hearing him. It's surreal."

When asked about a potential hostage deal and temporary cease-fire between Israel and Hamas, Siegel said that she does think an agreement "can be reached" and pointed to an earlier deal that secured the release of her aunt and others during a brief pause in the war late last year.

Siegel also said that she believes the new release of purported hostage videos shows that Hamas is signaling they are ready to make a deal.

But she said that she is concerned that it might not be in Israeli Prime Minister Benjamin Netanyahu's "political interest to close a deal," though Netanyahu has said his goal is freeing the captives in Gaza as well as dismantling Hamas.

Siegel said that the Biden administration should "think about what they can do directly to bring our American citizens home."

She also said she has felt the "commitment from the Biden administration to get him back," referring to her uncle.

She became emotional talking about how her family missed her uncle during their Passover celebration and had a picture of him to pay tribute.

"I think there's so much swirling in the political realm that it's easy to forget that these are human beings. Keith is a grandfather, he's a husband, he's a brother, he's an uncle," she said.

She was asked whether her family is worried if a potential Israeli invasion of the Gaza city of Rafah, to further target Hamas fighters, could threaten her uncle's safety. She responded that she and her family are "very concerned."

-ABC News' Michelle Stoddart

Hamas will send a delegation to Cairo, Egypt, on Monday to participate in hostage and cease-fire deal negotiations, ABC News has confirmed.

Meanwhile, a senior Hamas official also told the Agence France-Presse on Sunday that the organization has no significant problems with the proposed deal.

"The atmosphere is positive unless there are new obstacles from the Israeli side," the Hamas official said.

-ABC News' Nasser Atta and Yael Benaya

Osama Hamdan, a senior Hamas official, said in a statement that cease-fire negotiations with Israel will cease if it moves forward with its operation into Rafah.

"The Israeli enemy is trying to blackmail everyone with the Battle of Rafah," he said in a statement.

Hamdan told Lebanese TV late Wednesday that a cease-fire deal had not been reached and Hamas was still "studying the swap deal proposal."

"We have substantial notes on the proposal," Hamdan told Lebanese TV.

"We are studying the proposal and we will respond to it in a way that serves our goals."

-ABC News' Dia Ostaz, Ellie Kaufman and Ghazi Balkiz